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## If a, b, and c are three different positive. . .

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### Top Member

Vincen Legendary Member
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#### If a, b, and c are three different positive. . .

Fri Sep 29, 2017 7:03 pm
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c

The OA is A.

How can I prove that option A is the correct choice?

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sat Sep 30, 2017 3:09 am
Vincen wrote:
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?

(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c

The OA is A.

How can I prove that option A is the correct choice?
If a=5, b=11 and c=13, then all 3 values are prime, as is their sum:
5+11+13 = 29.

Thus, option A could be true.

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